Question 252733
Let's find the slope of the line through the points A(5,8) and B(7,11)


Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(5,8\right)]. So this means that {{{x[1]=5}}} and {{{y[1]=8}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(7,11\right)].  So this means that {{{x[2]=7}}} and {{{y[2]=11}}}.



{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula.



{{{m=(11-8)/(7-5)}}} Plug in {{{y[2]=11}}}, {{{y[1]=8}}}, {{{x[2]=7}}}, and {{{x[1]=5}}}



{{{m=(3)/(7-5)}}} Subtract {{{8}}} from {{{11}}} to get {{{3}}}



{{{m=(3)/(2)}}} Subtract {{{5}}} from {{{7}}} to get {{{2}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(5,8\right)] and *[Tex \LARGE \left(7,11\right)] is {{{m=3/2}}}



======================================================================


Now let's find the slope of the line through the points E(-1,-2) and F(-6,-4)



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-1,-2\right)]. So this means that {{{x[1]=-1}}} and {{{y[1]=-2}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-6,-4\right)].  So this means that {{{x[2]=-6}}} and {{{y[2]=-4}}}.



{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula.



{{{m=(-4--2)/(-6--1)}}} Plug in {{{y[2]=-4}}}, {{{y[1]=-2}}}, {{{x[2]=-6}}}, and {{{x[1]=-1}}}



{{{m=(-2)/(-6--1)}}} Subtract {{{-2}}} from {{{-4}}} to get {{{-2}}}



{{{m=(-2)/(-5)}}} Subtract {{{-1}}} from {{{-6}}} to get {{{-5}}}



{{{m=2/5}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-1,-2\right)] and *[Tex \LARGE \left(-6,-4\right)] is {{{m=2/5}}}